Rotary seals are often employed to seal about a round shaft element moving linearly; that is, axially, an undetermined distance, with or without the simultaneous rotation of the shaft about its axis. One of the problems associated with the rotary-type seal, wherein a shaft element moves linearly or axially, is the problem associated with the escape of the lubricant from the rotary-type seal during such linear motion. The escape of lubricant from rotary-type seals increases with the wear of the seal and is particularly a problem in connection with low-viscosity, ferrofluid-type, multiple-stage rotary seals, such as the type described in U.S. Pat. No. 3,620,584.